OF THE ROOTS OF SYSTEMS OP EQUATION'S. 
485 
Weight 1, 
Biweight 10 , Biweight 01 , 
(lo) ; (OT) ; 
Bi weight 20 , 
(50) 
( 10 "); 
Weight 2, 
Biweight 11 , 
(ii) 
(low); 
Bi weight 02 , 
( 02 ) 
(0T=>); 
Weight 3, 
Biweight 30, 
Biweight 21, 
Bi weight 12, 
Bi weight 03, 
(^) 
(W) 
(12) 
(03) 
(mTo) 
(M oT) 
(To 02 ) 
(Ol 02) 
(10*); 
(ITIo) 
(W U) 
(Ol*); 
(10* ol) ; 
(To oT*); 
Weight 4, 
Biweight 40, 
Bi weight 31, 
Bi weight 22, 
Bi weight 13, 
Bi weight 04, 
(4b) 
(3T) 
(22) 
(13) 
(bi) 
(3b lb) 
(2T Ib) 
(21 bl) 
(l2 bl) 
(b3 ol) 
(2b2) 
(3b bT) 
(12 Ib) 
(bblb) 
(022) 
(^ Ib^) 
(20 IT) 
(20 b2) 
(bill) 
(b2 bl2) 
(To"); 
(^Tbbl) 
(TT^') 
(bbibbi) 
(bl"). 
(TTIb^) 
(2b bi^) 
(TTbl^) 
(103 . 
(b2Tb2) 
(IbbT^); 
(iITbbI) 
(Tb^ bi^); 
§ 2 . Preliminary Algehraic Theory. 
7. The partitions with one bipart correspond to the sums of the powers in the 
single system, or unipartite theory. They are easily expressed in terms of the 
fundamental symmetric functions. 
